Proinov contractions and discontinuity at fixed point

Ravindra K. Bisht, R. P. Pant, Vladimir Rakočević

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245.

Original languageEnglish
Pages (from-to)131-137
Number of pages7
JournalMiskolc Mathematical Notes
Issue number1
Publication statusPublished - 2019
Externally publishedYes


  • (∈-δ) contractions
  • Fixed point
  • Orbital continuity
  • Power contraction

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Numerical Analysis
  • Discrete Mathematics and Combinatorics
  • Control and Optimization


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